1. 1.3. Equipartition Of Energy Per Molecule And Its Constituent Parts
 A Fundamental Problem

2. Gas molecules composed of several atoms
Equipartition theorem (see Part III)
Each quadratic term in H contributes kT /2 to <ε>
For each atom <ε> = 3kT /2.
For each molecule <K.E.>C.M. = 3kT /2.
Ideal gas law: PV = NkT = 2E / f.
E = total energy = N f kT /2
f = effective degrees of freedom of each molecule

3. Proof of (2) : <K.E.>C.M. = 3kT /2
From (1):
Hence:

4. vcm and vrel are independent: 

5. Proof of (3): PV = NkT = 2E / f
Elastic collisions:
For r atoms:
Adiabatic process:
See Exercise 1.8

7. Rotations and vibrations of a triatomic molecule
DoF = 33 = 9
Translation: 3
Rotation: 3
Vibration: 3

8. Heat Capacity Problem Experiment (Theory): For He,   1.660
For O2 ,   1.4
 f  5 (6)

9. Heat Capacity Problem  Failure of the Equipartition Theorem
Atom = ( Protons + Neutrons ) + electrons
 f  Z
Hadrons = Quarks f not known exactly
Explanation: States are quantized
 Degree of freedom is “frozen” if
Excitation energy >> Thermal energy

10. Diatomic Gas Low T Experiment: High T Experiment:  f  5  f  7
Theory:
K.E. + Vvib
f = = 7
Theory:
K.E. + Vvib
f = 5 + (1+1) = 5